A Simple Stochastic Variance Reduced Algorithm with Fast Convergence Rates
This work addresses the need for more adaptable and efficient optimization algorithms in machine learning, offering a simpler alternative that maintains high performance and extends to sparse and asynchronous settings, though it is incremental relative to existing methods.
The authors tackled the complexity of accelerated stochastic variance reduced gradient methods by introducing a simpler algorithm (MiG) that achieves the best-known convergence rates for both strongly convex and non-strongly convex problems, with practical improvements demonstrated in experiments for tasks like logistic regression.
Recent years have witnessed exciting progress in the study of stochastic variance reduced gradient methods (e.g., SVRG, SAGA), their accelerated variants (e.g, Katyusha) and their extensions in many different settings (e.g., online, sparse, asynchronous, distributed). Among them, accelerated methods enjoy improved convergence rates but have complex coupling structures, which makes them hard to be extended to more settings (e.g., sparse and asynchronous) due to the existence of perturbation. In this paper, we introduce a simple stochastic variance reduced algorithm (MiG), which enjoys the best-known convergence rates for both strongly convex and non-strongly convex problems. Moreover, we also present its efficient sparse and asynchronous variants, and theoretically analyze its convergence rates in these settings. Finally, extensive experiments for various machine learning problems such as logistic regression are given to illustrate the practical improvement in both serial and asynchronous settings.